An on-ground measurement of dust-particle residual charges in the afterglow of a dusty plasma was performed in a rf discharge. An upward thermophoretic force was used to balance the gravitational force. It was found that positively charged, negatively charged, and neutral dust particles coexisted for more than $1\min$ after the discharge was switched off. The mean residual charge for $200\text{−}\mathrm{nm}$-radius particles was measured. The dust particle mean charge is about $-5e$ at a pressure of $1.2\mathrm{mbar}$ and about $-3e$ at a pressure of $0.4\mathrm{mbar}$.

Random walks are developed to approximate the solutions of multiscaling, fractional-order, anomalous diffusion equations. The essential elements of the diffusion are described by the matrix-order scaling indexes and the mixing measure, which describes the diffusion coefficient in every direction. Two forms of the governing equation (also called the multiscaling fractional diffusion equation), based on fractional flux and fractional divergence, are considered, where the diffusion coefficient and the drift vary in space. The particle-tracking algorithm is also extended to approximate anomalous diffusion with a streamline-dependent mixing measure, using a streamline-projection technique. In this and other general cases, the random walk method is the only known way to solve the nonhomogeneous equations. Five numerical examples demonstrate the flexibility, simplicity, and efficiency of the random walk method.

The evolution of a colloidal fractal-like aggregate system is studied theoretically with account for the reduction of the single-particle concentration in the space between these growing aggregates. Two different mechanisms of the initial aggregate formation are considered. They are heterogeneous aggregation, when the initial aggregates appear on foreign nuclei (the biggest particles, pollution, etc.), and homogeneous nucleation, when the initial clusters appear due to a random meeting and combination of single Brownian particles. The principles of colloid supersaturation decrease and the aggregate distribution in size are obtained in both cases as well as the internal structure of the clusters. Unlike the usual condensation-type phase transition, the system of discrete clusters is formed at the final stage of the aggregation process. The internal particle distribution in these clusters does not obey the universal scaling power law, which differs from the model case of separate cluster growth in an infinite colloidal medium with permanent concentration of free particles.

We present molecular dynamics simulations of the slow dynamics of a mixture of large and small soft spheres with a large size disparity. The dynamics are investigated in a broad range of temperature and mixture composition. As a consequence of the large size disparity, large and small particles exhibit very different relaxation times. As previously reported for simple models of short-ranged attractive colloids and polymer blends, several anomalous dynamic features are observed: (i) sublinear behavior for mean-squared displacements, (ii) concave-to-convex crossover for density-density correlators, by varying the temperature or wave vector, and (iii) logarithmic decay for specific wave vectors of density-density correlators. These anomalous features are observed over time intervals extending up to four decades and strongly resemble predictions of the mode coupling theory (MCT) for state points close to higher-order MCT transitions, which originate from the competition between different mechanisms for dynamic arrest. For the large particles we suggest competition between soft-sphere repulsion and depletion effects induced by neighboring small particles. For the small particles we suggest competition between bulklike dynamics and confinement, respectively induced by neighboring small particles and by the slow matrix of large particles.

We measured the angular dependence of the 0th, $\pm 1$st, and $\pm 2$nd optical diffraction orders from a $50\mathrm{\mu }\mathrm{m}$ thick transmission grating recorded in a UV-curable holographic polymer-dispersed liquid crystal (HPDLC) made from commercially available constituents. The analysis was performed for two orthogonal polarizations of the probe beams. The emphasis was laid on the temperature dependence of the grating anisotropy. Above the nematic-isotropic phase transition, the grating is optically isotropic. At lower temperatures the grating strength for the optical polarization perpendicular to the grating vector decreases with decreasing temperature, while for orthogonal polarization it increases with decreasing temperature. As a consequence, a regime of diffraction with strongly overmodulated gratings is observed. Our investigations indicate that the anisotropy of the refractive-index modulation scales with the optical anisotropy of the liquid crystal medium forming the phase-separated domains. We further demonstrate that light scattering effects, which are profound only in the nematic phase, must not be neglected and can be taken into account via a Lorentzian line-shape broadening of the probing wave vector directions in the framework of the diffraction theory for anisotropic optical phase gratings.

We analyze and predict the behavior of a chirally imprinted elastomer under a mechanical strain and an electric field, applied along the helical axis. As the strain and/or field increases, the system is deformed from a conical or transverse imprinted state towards an ultimately nematic one. At a critical strain and/or field there is a first-order transition to a low imprinting efficiency state. This transition is accompanied by a discontinuous global rotation of the director toward the axis of the imprinted helix, measured by the cone angle, $\theta$. We show that the threshold electric field required for switching this transition can be conveniently low, provided an appropriate prestrain is imposed. We suggest that these properties may give rise to a “chiral pump.”

This work explains a mechanism through which the introduction of excitatory synaptic coupling between two model cells, one of which is excitable and the other of which is tonically active when uncoupled, leads to bursting in the resulting two-cell network. This phenomenon can arise when the individual cells are conditional relaxation oscillators, in that they can be tuned to engage in relaxation oscillations, or when they are conditional square-wave bursters. The mechanism is illustrated with a model for conditional pacemaker neurons in the pre-Bötzinger complex as well as with a reduced form of this model. In the relaxation oscillator case, a periodic bursting solution is proved to exist in the singular limit, under a pair of general conditions. These conditions relate the durations of the silent and active phases of the bursting solution to the locations of certain structures in the phase plane, at appropriate synaptic input strengths. Further, additional conditions on the relative flow rates in the silent and active phases are proved to imply the uniqueness and asymptotic stability of the bursting solution.

We show that abrupt structural transitions can arise in functionally optimal networks, driven by small changes in the level of transport congestion. Our results offer an explanation as to why so many diverse species of network structure arise in nature (e.g., fungal systems) under essentially the same environmental conditions. Our findings are based on an exactly solvable model system which mimics a variety of biological and social networks. We then extend our analysis by introducing a renormalization scheme involving cost motifs, to describe analytically the average shortest path across multiple-ring-and-hub networks. As a consequence, we uncover a “skin effect” whereby the structure of the inner multiring core can cease to play any role in terms of determining the average shortest path across the network.

A different approach will be presented that aims to scrutinize the phase-space trajectories of a general class of Hamiltonian systems with regard to their regular or irregular behavior. The approach is based on the “energy-second-moment map” that can be constructed for all Hamiltonian systems of the generic form $H={\mathit{p}}^2∕2+V(\mathit{q},t)$. With a three-component vector $\mathit{s}$ consisting of the system’s energy $h$ and second moments $\mathit{qp}$, ${\mathit{q}}^2$, this map linearly relates the vector $\mathit{s}\left(t\right)$ at time $t$ with the vector’s initial state $\mathit{s}\left(0\right)$ at $t=0$. It will turn out that this map is directly obtained from the solution of a linear third-order equation that establishes an extension of the set of canonical equations. The Lyapunov functions of the energy-second-moment map will be shown to have simple analytical representations in terms of the solutions of this linear third-order equation. Applying Lyapunov’s regularity analysis for linear systems, we will show that the Lyapunov functions of the energy-second-moment map yields information on the irregularity of the particular phase-space trajectory. Our results will be illustrated by means of numerical examples.

Considering almost all the effective processes of physics and chemical reaction in our numerical computation model, we investigate the mechanism of single bubble sonoluminescence (SBSL). For those sonoluminescing single bubbles in water at its flashing phase, the numerical simulation reveals that if the temperature inside the bubble is not high enough which may result in the plenty oxygen molecules and OH radicals undissociated, such as the case of a single argon bubble in $20°\mathrm{C}$ or $34°\mathrm{C}$ water, the radiative attachment of electrons to oxygen molecules and OH radicals contributes most to the SBSL; if the temperature inside the bubble is higher which makes most of the water vapor inside the bubble dissociate into oxygen and hydrogen atoms, such as the case of an argon bubble or a helium bubble in $0°\mathrm{C}$ water, the radiative attachment of electrons to oxygen and hydrogen atoms dominates the SBSL; if the temperature is still higher, such as the case of a xenon bubble in $0°\mathrm{C}$ water, the contribution from electron-neutral atom bremsstrahlung and electron-ion bremsstrahlung and recombination would be comparable with the contribution from the radiative attachment of electrons to oxygen and hydrogen atoms, and they together dominate the SBSL. For sonoluminescing single bubbles in those low vapor pressure liquids, such as in $85\mathrm{wt.}\%$ sulphuric acid, the electron-neutral atom bremsstrahlung and the electron-ion bremsstrahlung and recombination contribute most to the continuous spectrum part of SBSL. The present calculation also provides good interpretations to those observed phenomena, such as emitted photon numbers, the width of optical pulses, the blackbody radiation like spectra. The temperature fitted by the blackbody radiation formula is very different from that calculated by the gas dynamics equations. Besides, the effect of chemical dissociation on the shock wave is also discussed.

We describe wave propagation and soliton localization in photonic lattices, which are induced in a nonlinear medium by an optical interference pattern, taking into account the inherent lattice deformations at the soliton location. We obtain exact analytical solutions and identify the key factors defining soliton mobility, including the effects of gap merging and lattice imbalance, underlying the differences with discrete and gap solitons in conventional photonic structures.

With the help of the “neutral inclusion” concept, the conditions of electromagnetic wave transparency for multilayered spheres, coated spheroids, and general particulate composites are analytically derived in the quasistatic case. The basic idea is to make the effective material property of a composite region equal to that of the surrounding medium. The general full-wave analysis shows that the obtained quasistatic conditions are useful in designing the electromagnetically transparent materials.

We consider the dimer-monomer problem for the rectangular lattice. By mapping the problem into one of close-packed dimers on an extended lattice, we rederive the Tzeng-Wu solution for a single monomer on the boundary by evaluating a Pfaffian. We also clarify the mathematical content of the Tzeng-Wu solution by identifying it as the product of the nonzero eigenvalues of the Kasteleyn matrix.

The free energies of the fcc, bcc, hcp, and simple cubic phases for hard spheres are calculated as a function of density using the fundamental measure theory models of Rosenfeld et al. [Phys. Rev. E 55, 4245 (1997)], Tarazona [Phys. Rev. Lett. 84, 694 (2001)], and Roth et al. [J. Phys.: Condens. Matter 14, 12063 (2002)] in the Gaussian approximation. For the fcc phase, the present work confirms the vanishing of the Lindemann parameter (i.e., vanishing of the width of the Gaussians) near close packing for all three models and the results for the hcp phase are nearly identical. For the bcc phase and for packing fractions above $\eta \sim 0.56$, all three theories show multiple solid structures differing in the widths of the Gaussians. In all three cases, one of these structures shows the expected vanishing of the Lindemann parameter at close packing, but this physical structure is only thermodynamically favored over the unphysical structures in the Tarazona theory and even then, some unphysical behavior persists at lower densities. The simple cubic phase is stabilized in the model of Rosenfeld et al. for a range of densities and in the Tarazona model only very near close packing.

The Ginzburg-Landau free energy functional for hard spheres is constructed using the fundamental measure theory approach to density functional theory as a starting point. The functional is used to study the liquid-fcc solid planer interface and the properties of small solid clusters nucleating within a liquid. The surface tension for planer interfaces agrees well with simulation and it is found that the properties of the solid clusters are consistent with classical nucleation theory.

We study a model lipid bilayer composed of a mixture of two incompatible lipid types which have a natural tendency to segregate in the absence of membrane fluctuations. The membrane is mechanically characterized by a local bending rigidity $\kappa \left(\varphi \right)$ which varies with the average local lipid composition $\varphi$. We show, in the case where $\kappa$ varies weakly with $\varphi$, that the effective interaction between lipids of the same type either can be everywhere attractive or can have a repulsive component at intermediate distances greater than the typical lipid size. When this interaction has a repulsive component, it can prevent macrophase separation and lead to separation in mesophases with a finite domain size. This effect could be relevant to certain experimental and numerical observations of mesoscopic domains in such systems.

Motivated by the abundance of directed synaptic couplings in a real biological neuronal network, we investigate the synchronization behavior of the Hodgkin-Huxley model in a directed network. We start from the standard model of the Watts-Strogatz undirected network and then change undirected edges to directed arcs with a given probability, still preserving the connectivity of the network. A generalized clustering coefficient for directed networks is defined and used to investigate the interplay between the synchronization behavior and underlying structural properties of directed networks. We observe that the directedness of complex networks plays an important role in emerging dynamical behaviors, which is also confirmed by a numerical study of the sociological game theoretic voter model on directed networks.

Recent progress in integrated circuit technologies requires precise evaluation between dynamic characteristics and topological architecture design. In this paper, we have investigated the performance evaluation of network-on-chip (NoC) architectures constructed with diverse scale-free network topologies by dynamic packet traffic simulation and theoretical network analysis. Topological differences of scale-free networks are evaluated by the degree-degree correlations that indicate topological tendency between the degree of a node and that of the nearest neighbors. Our simulation results quantitatively show that the NoC architecture constructed with the topology where hubs mostly connect to lower-degree nodes is found to achieve short latency and low packet loss ratio since it can disperse traffic load and avoid the extreme concentration of load on hubs.

We present numerical and analytical studies of a quantum computer proposed by the Yamamoto group in Phys. Rev. Lett. 89, 017901 (2002). The stable and quantum chaos regimes in the quantum computer hardware are identified as a function of magnetic field gradient and dipole-dipole couplings between qubits on a square lattice. It is shown that a strong magnetic field gradient leads to suppression of quantum chaos.